An investment is worth $3518 in 1995. By 2000 it has grown to $5553. Let y be the value of the investment in the year x, where x = 0 represents 1995. Write a linear equation that models the value of the investment in the year x.

A. y = -407x + 7588
B. y =1/407 x + 3518
C. y = -407x + 3518
D. y = 407x + 3518
my guess is d but i am not sure and stuck on this question

since the investment grows linearly,

you have two points,
(0, 3518) and (5,5553)
slope = (5553-3518)/(5-0) = 407
looking at the choices, the only one possible is D, since it has a slope of +407
making sure, it is correct ....
y = 407x + b
and since (0,3518) would be the y-intercept
D is the correct choice

The slope of the line is

(5553-3518)/(2000-1995) = 407

That leaves only D as the choice.

You're almost there, but let's double-check the equation.

To find the equation that models the value of the investment, we need to find the slope and y-intercept.

The slope can be calculated by finding the difference in values between two known points. In this case, we have two points: (0, 3518) and (5, 5553). The year 2000 corresponds to x = 5, and the value is $5553.

Now let's calculate the slope:

slope = (change in y) / (change in x)
= (5553 - 3518) / (5 - 0)
= 2035 / 5
= 407

So the slope of the linear equation is 407.

To find the y-intercept, we can substitute one of the points into the equation and solve for y. Let's use the point (0, 3518).

y = mx + c
3518 = 407(0) + c
3518 = c

So, the y-intercept is 3518.

Putting it all together, the linear equation that models the value of the investment in the year x is:

y = 407x + 3518

So the correct answer is D.

You are correct! The linear equation that models the value of the investment in the year x is:

y = 407x + 3518

So, the correct answer is D.

To find the linear equation that models the value of the investment, we need to determine the relationship between the year and the value of the investment. We are given two data points: the investment is worth $3518 in 1995 (x = 0) and $5553 in 2000 (x = 5).

We can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:
m = (change in y) / (change in x)

Using the given data, the change in y is $5553 - $3518 = $2035, and the change in x is 5 - 0 = 5. Therefore, the slope is:
m = 2035 / 5 = 407

Now that we have the slope, we need to find the y-intercept, b. We can substitute one of the points (x, y) in the equation and solve for b.

Using the point (0, $3518):
y = mx + b
$3518 = 407(0) + b
$3518 = b

So, the equation becomes:
y = 407x + $3518 (D)

Therefore, your guess is correct, and the linear equation that models the value of the investment in the year x is y = 407x + $3518.